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Operating regimes of signaling cycles: statics, dynamics, and noise filtering.

Gomez-Uribe C, Verghese GC, Mirny LA - PLoS Comput. Biol. (2007)

Bottom Line: These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions.Numerical simulations show that our analytical results hold well even for noise of large amplitude.We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

View Article: PubMed Central - PubMed

Affiliation: Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.

ABSTRACT
A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input-output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input-output characteristics. These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act--in all four regimes--as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

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Related in: MedlinePlus

Relative ErrorThe relative error between the steady-state characteristic of the hyperbolic (A), signal-transducing (B), threshold-hyperbolic (C), and ultrasensitive (D) regimes, and that of the tQSSA in Equation 3 are shown. To compute the error for a regime, we first approximated the average squared difference between the regime's steady state and that of Equation 3 and then divided its square root by the total substrate S1. A relative error of 0.1 then corresponds to an average absolute difference between the steady-state characteristic of the regime and that of Equation 3 of 0.1St (see Text S5). The figures here show that the relative error for each regime is small for a wide region of the K1 versus K2 space, demonstrating that the four regimes cover almost the full space. The parameters used for this cycle are the same as those in Figure 2D, except K1 and K2, which were varied in the range of values shown in the x and y axes in this figure. The dashed lines enclose the regions where each regime is expected to describe the system well.
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pcbi-0030246-g003: Relative ErrorThe relative error between the steady-state characteristic of the hyperbolic (A), signal-transducing (B), threshold-hyperbolic (C), and ultrasensitive (D) regimes, and that of the tQSSA in Equation 3 are shown. To compute the error for a regime, we first approximated the average squared difference between the regime's steady state and that of Equation 3 and then divided its square root by the total substrate S1. A relative error of 0.1 then corresponds to an average absolute difference between the steady-state characteristic of the regime and that of Equation 3 of 0.1St (see Text S5). The figures here show that the relative error for each regime is small for a wide region of the K1 versus K2 space, demonstrating that the four regimes cover almost the full space. The parameters used for this cycle are the same as those in Figure 2D, except K1 and K2, which were varied in the range of values shown in the x and y axes in this figure. The dashed lines enclose the regions where each regime is expected to describe the system well.

Mentions: The four regimes we consider, although obtained only at extreme parameter values, are actually quite descriptive of the system for a wide range of parameters, and naturally partition the space of possible steady-state behaviors of the signaling cycle into quadrants, as shown Figure 3. Figure 3 shows the relative error between the steady-state characteristic of each of the four regimes and that of Equation 3 for a wide range of kinase and phosphatase MM constants (see Text S4). It reveals that the regime approximations are quite good at a wide range of values of MM constant (for example, the region with a relative error of less than 10% for each regime covers almost a full quadrant in the plots), and not only when the MM constants take the very large or very small values required in the regime definitions. This demonstrates that these four regimes, though defined by extreme values of system parameters, actually encompass the full space of cycle behaviors.


Operating regimes of signaling cycles: statics, dynamics, and noise filtering.

Gomez-Uribe C, Verghese GC, Mirny LA - PLoS Comput. Biol. (2007)

Relative ErrorThe relative error between the steady-state characteristic of the hyperbolic (A), signal-transducing (B), threshold-hyperbolic (C), and ultrasensitive (D) regimes, and that of the tQSSA in Equation 3 are shown. To compute the error for a regime, we first approximated the average squared difference between the regime's steady state and that of Equation 3 and then divided its square root by the total substrate S1. A relative error of 0.1 then corresponds to an average absolute difference between the steady-state characteristic of the regime and that of Equation 3 of 0.1St (see Text S5). The figures here show that the relative error for each regime is small for a wide region of the K1 versus K2 space, demonstrating that the four regimes cover almost the full space. The parameters used for this cycle are the same as those in Figure 2D, except K1 and K2, which were varied in the range of values shown in the x and y axes in this figure. The dashed lines enclose the regions where each regime is expected to describe the system well.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2230677&req=5

pcbi-0030246-g003: Relative ErrorThe relative error between the steady-state characteristic of the hyperbolic (A), signal-transducing (B), threshold-hyperbolic (C), and ultrasensitive (D) regimes, and that of the tQSSA in Equation 3 are shown. To compute the error for a regime, we first approximated the average squared difference between the regime's steady state and that of Equation 3 and then divided its square root by the total substrate S1. A relative error of 0.1 then corresponds to an average absolute difference between the steady-state characteristic of the regime and that of Equation 3 of 0.1St (see Text S5). The figures here show that the relative error for each regime is small for a wide region of the K1 versus K2 space, demonstrating that the four regimes cover almost the full space. The parameters used for this cycle are the same as those in Figure 2D, except K1 and K2, which were varied in the range of values shown in the x and y axes in this figure. The dashed lines enclose the regions where each regime is expected to describe the system well.
Mentions: The four regimes we consider, although obtained only at extreme parameter values, are actually quite descriptive of the system for a wide range of parameters, and naturally partition the space of possible steady-state behaviors of the signaling cycle into quadrants, as shown Figure 3. Figure 3 shows the relative error between the steady-state characteristic of each of the four regimes and that of Equation 3 for a wide range of kinase and phosphatase MM constants (see Text S4). It reveals that the regime approximations are quite good at a wide range of values of MM constant (for example, the region with a relative error of less than 10% for each regime covers almost a full quadrant in the plots), and not only when the MM constants take the very large or very small values required in the regime definitions. This demonstrates that these four regimes, though defined by extreme values of system parameters, actually encompass the full space of cycle behaviors.

Bottom Line: These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions.Numerical simulations show that our analytical results hold well even for noise of large amplitude.We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

View Article: PubMed Central - PubMed

Affiliation: Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.

ABSTRACT
A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input-output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input-output characteristics. These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act--in all four regimes--as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

Show MeSH
Related in: MedlinePlus